math help

What is 5/11 + 10/12?

What is 5/11 + 10/12?

This is how we add

5
11
 +
10
12

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 5 by 12, and get 60, then we multiply 11 by 12 and get 132.

5/11 times 12

Do the same for the second term. We multiply 10 by 11, and get 110, then multiply 11 by 12 and get 132.

10/12 times 11

The problem now has new fractions to add:

60
132
 +
110
132

Step 2

Since our denominators match, we can add the numerators.

60 + 110 = 170

The sum we get is

170
132

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

170
132
 ÷ 2 =
85
66

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. So next you try the next prime number, which is 53...

No good. So next you try the next prime number, which is 59...

No good. So next you try the next prime number, which is 61...

No good. So next you try the next prime number, which is 67...

No good. 67 is larger than 66. So we're done reducing.

And we're done! Here's the final answer to 5/11 + 10/12

5
11
 +
10
12
 =
85
66
© 2014 Randy Tayler

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